A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi

Thermonuclear burst physics with RXTE

Recently we have made measurements of thermonuclear burst energetics and recurrence times which are unprecedented in their precision, largely thanks to the sensitivity of the Rossi X-ray Timing Explorer. In the "Clocked Burster", GS 1826-24, hydrogen burns during the burst via the rapid-proton (rp) process, which has received particular attention in recent years through theoretical and modelling studies. The burst energies and the measured variation of alpha (the ratio of persistent to burst flux) with accretion rate strongly suggests solar metallicity in the neutron star atmosphere, although this is not consistent with the corresponding variation of the recurrence time. Possible explanations include extra heating between the bursts, or a change in the fraction of the neutron star over which accretion takes place. I also present results from 4U 1746-37, which exhibits regular burst trains which are interrupted by "out of phase" bursts.Comment: 4 pages, 2 figures, AIP conference proceedings format. To appear in the proceedings of the "X-ray Timing 2003: Rossi and Beyond" meeting held in Cambridge, MA, November, 200

Uniqueness of de Sitter space

All inextendible null geodesics in four dimensional de Sitter space dS^4 are complete and globally achronal. This achronality is related to the fact that all observer horizons in dS^4 are eternal, i.e. extend from future infinity scri^+ all the way back to past infinity scri^-. We show that the property of having a null line (inextendible achronal null geodesic) that extends from scri^- to scri^+ characterizes dS^4 among all globally hyperbolic and asymptotically de Sitter spacetimes satisfying the vacuum Einstein equations with positive cosmological constant. This result is then further extended to allow for a class of matter models that includes perfect fluids.Comment: 22 pages, 2 figure

A simple proof of the recent generalisations of Hawking's black hole topology theorem

A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking's argument, Gibbons and Woolgar could also show the existence of a genus dependent lower bound for the entropy of topological black holes with negative cosmological constant. Recently Hawking's black hole topology theorem, along with the results of Gibbons and Woolgar, has been generalised to the case of black holes in higher dimensions. Our aim here is to give a simple self-contained proof of these generalisations which also makes their range of applicability transparent.Comment: 12 pages, 1 figur

Non-Existence of Black Holes in Certain Λ<0\Lambda<0 Spacetimes

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular (i.e., nondegenerate) black holes in spacetimes with a negative cosmological constant, given that the fundamental group of space is infinite. We use this to rule out the existence of regular negative mass AdS black holes with Ricci flat scri. For any mass, we also rule out a class of conformally compactifiable static black holes whose conformal infinity has positive scalar curvature and infinite fundamental group, subject to our asymptotic conditions. In a limited, but important, special case our result adds new support to the AdS/CFT inspired positive mass conjecture of Horowitz and Myers.Comment: 17 pages, Latex. Typos corrected, minor changes to the text. Accepted for publication in Classical and Quantum Gravit

Nonexistence of marginally trapped surfaces and geons in 2+1 gravity

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the dominant energy condition with cosmological constant \Lambda \geq 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2+1 gravity but also apply to quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have been combined to give a single proof, thereby circumventing an issue with the second proof associated with potential blow-ups of solutions to Jang's equation. To appear in Commun. Math. Phy

Fingerprinting the impacts of global change on tropical forests

Recent observations of widespread changes in mature tropical forests such as increasing tree growth, recruitment and mortality rates and increasing above-ground biomass suggest that 'global change' agents may be causing predictable changes in tropical forests. However, consensus over both the robustness of these changes and the environmental drivers that may be causing them is yet to emerge. This paper focuses on the second part of this debate. We review (i) the evidence that the physical, chemical and biological environment that tropical trees grow in has been altered over recent decades across large areas of the tropics, and (ii) the theoretical, experimental and observational evidence regarding the most likely effects of each of these changes on tropical forests. Ten potential widespread drivers of environmental change were identified: temperature, precipitation, solar radiation, climatic extremes (including El Niño Southern Oscillation events), atmospheric CO2 concentrations, nutrient deposition, O3/acid depositions, hunting, land-use change and increasing liana numbers. We note that each of these environmental changes is expected to leave a unique 'fingerprint' in tropical forests, as drivers directly force different processes, have different distributions in space and time and may affect some forests more than others (e.g. depending on soil fertility). Thus, in the third part of the paper we present testable a priori predictions of forest responses to assist ecologists in attributing particular changes in forests to particular causes across multiple datasets. Finally, we discuss how these drivers may change in the future and the possible consequences for tropical forests

What’s in It for Me? Reciprocal Exchanges between Underwriters and Venture Capitalists

In this article, we examine the impact of repeat interactions between VCs and underwriters. Past research has suggested that such interactions build trust and may contribute to more equitable treatment of issuing firms. We adopt an alternative perspective and suggest that these repeat interactions are characterized by reciprocal exchanges facilitated by opportunistic behavior from the VC. Our analysis demonstrates that VCs and underwriters interact in order to appropriate greater value from the IPO. This article provides a more complete understanding of repeat interactions between the VC and the underwriter by identifying characteristics of the relationship that have an impact on the value of the IPO

Summary of the recent short-haul systems studies

The results of several NASA sponsored high density short haul air transportation systems studies are reported as well as analyzed. Included are the total STOL systems analysis approach, a companion STOL composites study conducted in conjunction with STOL systems studies, a STOL economic assessment study, an evaluation of STOL aircraft with and without externally blown flaps, an alternative STOL systems for the San Francisco Bay Area, and the quiet, clean experimental engine studies. Assumptions and results of these studies are summarized, their differences, analyzed, and the results compared with those in-house analyses performed by the Systems Studies Division of the NASA-Ames Research Center. Pertinent conclusions are developed and the more significant technology needs for the evaluation of a viable short haul transportation system are identified